I was head TF for QR28: Magic of Numbers in the fall of 2008, working with Michael Hopkins and Jesse Kass. You can find the syllabus here, some notes on the Chinese Remainder Theorem here, and the homework and practice exams below.
All references are to The Magic of Numbers by Gross and Harris (see Text).
| Mon | Sept 15 | The Fibonacci Sequence. | No Homework. | |
| Wed | Sept 17 | Part 1. Counting. Simple counting. Chapter 1. | Homework 1. | Solution 1. |
| Fri | Sept 19 | More on counting. Introduction to Probability. | Homework 2. | Solution 2. |
| Mon | Sept 22 | The Multiplication principle. Chapter 2. | Homework 3. | Solution 3. |
| Wed | Sept 24 | The Subtraction principle. Chapter 3. | Homework 4. | Solution 4. |
| Fri | Sept 26 | How to count collections of objects. Chapter 4. | Homework 5. | Solution 5. |
| Mon | Sept 29 | More on counting collections. Probability. Chapters 4 & 5. | Homework 6. | Solution 6. |
| Wed | Oct 1 | Probability continued. Chapter 5. | Homework 7. | Solution 7. |
| Fri | Oct 3 | Pascal's Triangle and the Binomial Theorem. Chapter 6. | Homework 8. | Solution 8. |
| Mon | Oct 6 | Review. | Practice Exam. | Solutions. |
| Wed | Oct 8 | Midterm 1. | ||
| Fri | Oct 10 | Part II. Arithmetic. Divisibility and Euclid's Algorithm. Chapter 8. | Homework 9. | Solution 9. |
| Mon | Oct 13 | Columbus Day. University Holiday. | No class. | |
| Wed | Oct 15 | More on Euclid's Algorithm. Chapter 8. | Homework 10. | Solution 10. |
| Fri | Oct 17 | Combinations. Chapter 9. | Homework 11. | Solution 11. |
| Mon | Oct 20 | Solving Diophantine equations. Chapter 9. Primes. Sections 10.1 and 10.2. | Homework 12. | Solution 12. |
| Wed | Oct 22 | Prime and composite numbers. The Sieve of Eratosthenes. Chapter 10. | Homework 13. | Solution 13. |
| Fri | Oct 24 | Factorization. Chapter 11. | Homework 14. | Solution 14. |
| Mon | Oct 27 | Consequences of unique factorization. Chapter 12. | Homework 15. | Solution 15. |
| Wed | Oct 29 | Part III. Modular Arithmetic. Arithmetic mod n. Chapters 14 and 15. | Homework 16. | Solution 16. |
| Fri | Oct 31 | Another way to look at modular arithmetic. Chapter 16. | Homework 17. | Solution 17. |
| Mon | Nov 3 | Dividing in modular arithmetic. Chapter 17. | Homework 18. | Solution 18. |
| Wed | Nov 5 | Calculating powers in modular arithmetic. Chapter 18. | Homework 19. | Solution 19. |
| Fri | Nov 7 | Fermat's Theorem. Calculating high powers in modular arithmetic. Chapter 18. | Homework 20. | Solution 20. |
| Mon | Nov 10 | Review. | Practice Exam. | Solutions. |
| Wed | Nov 12 | Midterm 2. | ||
| Fri | Nov 14 | Computing roots in modular arithmetic. Chapter 19. | Homework 21. | Solution 21. |
| Mon | Nov 17 | Chapter 19. Computing roots again. | Homework 22. | Solution 22. |
| Wed | Nov 19 | Chinese Remainder Theorem. | Homework 23. | Solution 23. |
| Fri | Nov 21 | Euler's function. Chapter 13. | Homework 24. | Solution 24. |
| Mon | Nov 24 | Euler's Theorem. Chapter 20. | Homework 25. | Solution 25. |
| Wed | Nov 26 | More Chinese Remainder Theorem, multiplicative orders. | No Homework. | Enjoy the break! |
| Fri | Nov 28 | Thanksgiving Recess. | No class. | |
| Mon | Dec 1 | Part IV. Codes and Primes. Types of codes. Chapter 21. | Frxdirsn 26. | Solution 26. |
| Wed | Dec 3 | Public-key cryptography. Chapter 22. | Homework 27. | Solution 27. |
| Fri | Dec 5 | Distribution of primes. Chapter 23. | Homework 28. | Solution 28. |
| Mon | Dec 8 | How to find large primes. Miller-Rabin test. Chapter 23. | Homework 29. | Solution 29. |
| Wed | Dec 10 | Generators. Chapters 24. | Homework 30. | Solution 30. |
| Fri | Dec 12 | Square roots of -1. Passwords. Chapter 24. | No Homework. | |
| Mon | Dec 15 | No class. Happy Holidays! | ||
| Final Review | Practice Exam |